A coronary artery bypass graft (CABG) procedure is a common surgical procedure in which a graft vessel, such as a saphenous vein or mammary artery, is connected surgically to a target vessel, or between two target vessels. Typically, the patient's chest is opened in order to perform this procedure, whether it is performed as a stopped-heart or beating-heart procedure. Opening the chest creates a major trauma from which it takes the patient some time to heal. Additionally, the patient is left with a large scar, and may have lasting pain. Attempts have been made to perform the CABG procedure in a minimally-invasive manner, using tools inserted through incisions in the thoracic cavity and/or percutaneously. However, such attempts have not met with significant acceptance by cardiac surgeons, due to problems inherent in the previous minimally-invasive procedures. One problem is that such procedures may utilize traditional rigid stabilizers that immobilize a portion of the heart, such as by pressing down on it or lifting up a portion of the surface, such that the heart cannot move freely during the anastomosis procedure. Rigid stabilizers are fixed rigidly to a retractor or other structure that itself is substantially fixed. However, fibrillation often results from such attempts to immobilize a portion of the heart. Fibrillation complicates the CABG procedure at best and is potentially fatal at worst. Another problem is that robotic devices that may be used for minimally-invasive surgery are expensive capital goods that some hospitals may not be able to afford. Such robotic devices may be capable of compensating for the motion of the heart by using software that measures the motion of the heart and adds a motion component to a robotic manipulator that cancels out at least some of the motion of that manipulator relative to the heart. However, such compensation is complex, and adds to the complexity and expense of the robotic device. Further, the manipulators used to perform the surgery are typically complex and expensive. As a result of the complexity of the robotic devices, surgeons typically require a significant amount of training time on them to become proficient, time which takes them away from their practices.